Optimization of the residence time of a Brownian particle in a spherical subdomain

TL;DR

This paper investigates how the residence time of a Brownian particle within a spherical subdomain can be optimized by adjusting the diffusion coefficient, with implications for various experimental setups.

Contribution

It introduces a method to optimize the residence time of Brownian particles by tuning the diffusion coefficient, considering different initial conditions and observation times.

Findings

Residence time can be maximized by selecting an optimal diffusion coefficient.

The effect varies with the nature of the initial position and observation time.

Potential applications in experimental design and particle tracking.

Abstract

In this communication, we show that the residence time of a Brownian particle, defined as the cumulative time spent in a given region of space, can be optimized as a function of the diffusion coefficient. We discuss the relevance of this effect to several schematic experimental situations, classified in the nature -- random or deterministic -- both of the observation time and of the starting position of the Brownian particle.